Theodor W. Hänsch and John L. Hall were awarded the Nobel Prize in Physics in 2005 for precision spectroscopy on the basis of highly precise optical frequency combs. Using such frequency combs, it is possible not only to measure fundamental constants with a high accuracy, but it is also possible to determine the difference between matter and antimatter. Such frequency combs are moreover very important in technical applications. By way of example, data transmission in optical fibers by means of “wavelength division multiplexing” (WDM) is based upon a frequency comb. Many other technical applications, such as radio-over-fiber systems, microwave photonics, and quasi-light-storage, also require precise, tunable frequency combs.
The following applies to such frequency combs: if all frequencies of the frequency comb have a fixed phase relation to one another, the time representation of the comb is a pulse train. If, moreover, all frequencies have the same amplitude and the same or a linearly displaced phase and if simultaneously unwanted frequency components are strongly damped, the time representation of this quasi-rectangular frequency comb is a cardinal sine (sinc) pulse train, where the following applies: sinc(x)=sin(x)/x. The sinc function is the Fourier transform of the rectangular function.
Sinc pulses are of particular importance in order to be able to increase the bit rates in future communication networks because sinc pulses enable information transmission with a maximum symbol rate. Whereas pure sinc pulses are non-causal and therefore not realizable, it is possible, by contrast, to realize a sinc pulse train by means of a frequency comb. For communication purposes, this pulse train has the same advantages as the individual pulses. Since the pulses of the sinc pulse train satisfy the Nyquist ISI criterion, these are also referred to as Nyquist pulses.
“Optical sinc-shaped Nyquist pulses of exceptional quality” by Marcelo A. Soto, Mehdi Alem, Mohammad Amin Shoaie, Armand Vedadi, Camille-Sophie Brés, Luc Thévenaz and Thomas Schneider describes a possibility for producing Nyquist pulse trains. A frequency comb with nine lines is generated in one embodiment by means of a laser by virtue of the individual line taken from the laser being provided with two side-lines by modulation, wherein these three lines are in turn respectively equipped with two side-lines by a second modulation cascade. All lines generated thus have the same spacing. In order to generate the necessary approximately equal phase between the lines, however, the phase difference between the modulated radiofrequency signals must be set precisely to compensate for propagation time differences. The bandwidth is also restricted to a relatively small bandwidth of approximately 160 GHz as a result of the modulators.
It is now known that mode-locked lasers generate a frequency comb. Such a frequency comb does not, however, have a rectangular form and the spacing between the individual frequency lines is fixedly predetermined by the repetition rate of the laser. This makes these frequency combs unsuitable for many applications. Another option consists of coupling phase modulators to one another, or to intensity modulators, and to thereby generate a frequency comb. Phase modulators cannot, however, be used to generate rectangular frequency combs. The maximum bandwidth obtainable by these frequency combs is also restricted by the bandwidth of the employed modulators.
It was until now only possible to generate approximately ideal sinc pulses with a maximum bandwidth of approximately 160 GHz (see above), corresponding to a temporal full width at half maximum (FWHM) duration of the pulses of approximately 6 ps. The maximum number of the lines of a frequency comb is also restricted, with the number of lines defining the repetition rate of the sinc pulses. However, for specific applications, such as, for example, for generating arbitrary pulse shapes, a number of lines which is as high as possible and a short duration of the pulses is desired.